Question - More than one confidence interval. As we prepare to take a sample and compute a 95% confidence interval, we know that the probability that the interval we compute will cover the parameter is 0.95. That's the meaning of 95% confidence. If we use several such intervals, however, our confidence that all of them give correct results is less than 95%. Suppose that we take independent samples each month for five months and report a 95% confidence interval for each set of data.
(a) What is the probability that all five intervals cover the true means? This probability (expressed as a percent) is our overall confidence level for the five simultaneous statements.
(b) What is the probability that at least four of the five intervals cover the true means?